Abstract
The article considers the urgent problem of optimizing the flight trajectory of unmanned aerial vehicles (UAVs) with given final conditions. An approach to constructing the optimal UAV trajectory along successive sections using approximation by a fifth-degree polynomial is presented. A mathematical model is developed that takes into account the features of using local inertial coordinate systems on each section of the trajectory. A motion optimization method is proposed based on minimizing the quadratic functional characterizing both the accuracy of reaching specified points and the energy costs for control. The solution to the optimization problem is obtained using analytical design of the optimal controller. Analytical expressions are given for determining the optimal lateral acceleration of the UAV, ensuring the required positioning accuracy with minimal energy costs. Features of coordinate transformation between trajectory sections to ensure continuity of motion are considered. A practical example of calculating the optimal UAV trajectory with given initial conditions is given.